I am married and currently living in a seperate house where my parents comes to visit occasionally. We have a cat which is paralysed and my wife is taking care of the cat. However, my parents hated any pets and blackmailed me that if i did not send the cat away, they will not come to visit us and i am unfilial to my parents. I am confused now, would like your advice on this

Your kinship with your parents comes first however there is no need on their part to lay such condition certainly not over a cat